What is the value of tan((5pi)/2)-2pi ?

The value of tan((5pi)/2)-2pi is Undefined

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tan((5pi)/2)-2pi

tan (\frac{5 π}{2}) - 2 π

Undefined

Solution steps

tan (\frac{5 π}{2}) - 2 π

Rewrite using trig identities:

tan (\frac{5 π}{2}) =

Undefined

tan (\frac{5 π}{2})

tan (\frac{5 π}{2}) = tan (\frac{π}{2})

tan (\frac{5 π}{2})

Rewrite

\frac{5 π}{2}

π \cdot 2 + \frac{π}{2}

= tan (π 2 + \frac{π}{2})

Apply the periodicity of

tan

tan (x + π \cdot k) = tan (x)

tan (π \cdot 2 + \frac{π}{2}) = tan (\frac{π}{2})

= tan (\frac{π}{2})

= tan (\frac{π}{2})

tan (\frac{π}{2})

is undefined

= Undefined

= Undefined

\frac{1}{cos ^{2} ( \frac{3 π}{4} )}

sin (\frac{1}{2})

sec^{2} (2 \cdot \frac{π}{6})

tan (6 0^{\circ}) + 2 tan (3 0^{\circ})

\frac{18}{cos ( 43. 4 ^{\circ} )}

What is the value of tan((5pi)/2)-2pi ?
The value of tan((5pi)/2)-2pi is Undefined